Liquid pump

ABSTRACT

In a liquid pump, n sets of concavities are formed in an outer circumference of an impeller. In a case where an angle between an i th  first line and an i th  second line is a pitch angle θ i  and an i th  difference of adjacent pitch angles is σ i  (σ i =θ i+1 −θ i ) (the i may be any integer of 1 to n), the pitch angles θ i  may be inhomogeneous. For each of the pitch angles θ i , there may be one or more other pitch angle θ k  (the k maybe any integer of 1 to n and other than i) being equal to the pitch angle θ i . Formulas 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35 may be satisfied.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Japanese Patent Application No. 2009-257629, filed on Nov. 11, 2009, the contents of which are hereby incorporated by reference into the present application.

TECHNICAL FIELD

The present specification discloses a technique for reducing a noise generated in a liquid pump.

DESCRIPTION OF RELATED ART

A liquid pump comprising an impeller of which a plurality of concavities is formed in an outer circumference is known. In this type of the liquid pump, liquid is sucked from a suction opening of a pump casing to an inside of the pump casing by a rotation of the impeller. Pressure of the liquid sucked into the inside of the pump casing is raised while the liquid flows through a flow path within the pump casing. The liquid with raised pressure is discharged from a discharge opening to an outside of the pump casing.

Pressure of the liquid at a discharge opening side of the flow path is greater than pressure of the liquid at a suction opening side of the flow path. Therefore, the liquid needs to be prevented to flow from the discharge opening side toward the suction opening side of the flow path.

Accordingly, an isolating wall for isolating the flow path on the discharge opening side from the flow path on the suction opening side is usually disposed close to the outer circumference edge of the impeller in the pump casing. Hence, in a case where the liquid pump comprises an impeller of which a plurality of concavities is formed by a regular pitch angle, the plurality of concavities passes by the isolating wall at a constant frequency (i.e., at constant time intervals) in accordance with the rotation of the impeller. As a result, a large noise in a frequency determined by a number of the rotation of the impeller and the pitch angle of the plurality of the concavities is generated in the liquid pump. The pitch angle means an angle between a first line and a second line when the impeller is viewed in plan view. The first line is a line connecting a rotation center of the impeller and a center in a circumferential direction of the impeller of a first concavity of the plurality of the concavities. The second line is a line connecting the rotation center of the impeller with a center in the circumferential direction of the impeller of a second concavity, adjacent the first concavity, of the plurality of the concavities. To address the above-Mentioned situation, a technique for reducing the noise generated in the liquid pump has been developed.

A liquid pump disclosed in Japanese patent application publication No. 11-50990 comprises an impeller in which all of the pitch angles θ are respectively different. The pitch angles θ are formed such as to satisfy a predetermined condition. The above Japanese patent application publication describes that a cycle by which the concavity passes by the isolating wall is not constant so as to reduce the noise in the liquid pump.

SUMMARY

Although the noise may be reduced to some degree by the above-mentioned technique, a technique in order to further reduce the noise is desired. The present application provides a technique for reducing the noise generated in the liquid pump.

Inventors have conducted various studies regarding reduction of the noise (noise pressure) generated in the liquid pump. As a result, the inventors have found a correlation between the noise generated in the liquid pump and a pressure variation of the liquid within the concavities. Furthermore, the inventors have found that reducing a spectrum peak value of the pressure variation of the liquid within the concavities is effective in reducing the noise generated in the liquid pump. The inventors have found barometers (indexes) which are strongly correlated with the spectrum peak value of the pressure variation of the liquid. Further, the inventors have studied a relationship between the barometers and the spectrum peak value of the pressure variation, and have specified a range of the barometers which reduces the spectrum peak value of the pressure variation.

The present specification discloses a liquid pump. This liquid pump may comprise a pump casing and an impeller rotatably disposed within the casing. When the impeller rotates, liquid is sucked into the pump casing and raise a pressure of the liquid within the pump casing so as to discharge the liquid with raised pressure out from the pump casing. In the liquid pump, n sets of concavities are formed in an outer circumference of the impeller, where the n is an integer of 2 or more. In a case where an angle between an i^(th) first line and an i^(th) second line is a pitch angle θ_(i) and an i^(th) difference of adjacent pitch angles is σ_(i) (σ_(i)=θ_(i+1)−θ_(i)), the pitch angles θ_(i) may be inhomogeneous, and for each of the pitch angles θ_(i), there may be one or more other pitch angle θ_(k) being equal to the pitch angle θ_(i), where the k is any integer of 1 to n and other than i. The i^(th) first line is a line connecting a rotation center of the impeller and a center of i^(th) concavity in a circumferential direction of the impeller. I.e., the i is any integer of 1 to n. The i^(th) second line is a line connecting the rotation center of the impeller with a center of i+1^(th) concavity in the circumferential direction of the impeller, where in case of i+1=n+1, then i+1=1. Further, following formulas (conditions) (1) and (2) may be satisfied.

0.05≦σ′/(average of θ)≦0.30  (1)

0.15≦C′≦0.35  (2)

Note that σ′, average of θ and C′ are defined by following formulas. In addition, any one concavity of the plurality of the concavities is numbered a first concavity, and the concavity number is given in ascending sequence along a rotation direction or a reverse direction of the rotation direction of the impeller.

${{average}\mspace{14mu} {of}\mspace{14mu} \theta \text{:}\mspace{14mu} \overset{\_}{\theta}} \equiv {\sum\limits_{i = 1}^{n}\; {\theta_{i}/n}}$ $\sigma^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\sigma_{i} - \overset{\_}{\sigma}} \right)^{2}} \right)/n}$ $\overset{\_}{\sigma} \equiv {\sum\limits_{i = 1}^{n}\; {\sigma_{i}/n}}$ $C^{\prime} \equiv \sqrt{\sum\limits_{j = 1}^{n}\; {\left( C_{j} \right)^{2}/n}}$ $C_{j} \equiv {\frac{1}{n\; \theta^{\prime \; 2}}{\sum\limits_{i = 1}^{n}\; {\left( {\theta_{i} - \overset{\_}{\theta}} \right) \cdot \left( {\theta_{i + j} - \overset{\_}{\theta}} \right)}}}$ $\theta^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\theta_{i} - \overset{\_}{\theta}} \right)^{2}} \right)/n}$

The inventors have found that σ′/(average of θ) and C′ are strongly correlated with the spectrum peak value of the pressure variation of the liquid within the concavities. Furthermore, in a case where the σ′/(average of θ) and C′ satisfy the above mentioned ranges (i.e., the above mentioned formulas (1) and (2) respectively), it has been found that a greater reduction of the noise generated in the liquid pump than the conventional art can be achieved. For each of the pitch angles θ_(i) (i=any of 1 to n), there may be one or more other pitch angle θ_(k) (the k is any integer of 1 to n and other than i) being equal to the pitch angle θ_(i). If there is no pitch angle being equal to the pitch angle θ_(i), when the impeller rotates, a pressure variation by the pitch angles θ_(i) is generated, and this pressure variation cannot be reduced. That is, a noise component by the pitch angle θ_(i) is not reduced. Meanwhile, if a plurality of the pitch angles is identical, e.g., the pitch angle θ_(i) is equal to the pitch angle θ_(k), a noise component generated when one concavity formed by the pitch angle θ_(i) passes by the isolating wall may be reduced by a noise component generated when another concavity formed by the pitch angle θ_(k) passes the isolating wall. The noise attributed to the specific pitch angle θ_(i) may be reduced by satisfying the above condition (i.e., one or more other pitch angle θ_(k) being equal to the pitch angle θ_(i)) and the above conditions of σ′/(average of θ) and C′.

In the liquid pump, a following formula (3) may be further satisfied.

0.1<(a number of pitch angles being equal to each other)/n<0.5  (3)

According to this constitution, the noise generated in the liquid pump may further be reduced without reducing pump efficiency of the liquid pump to a great degree.

According to the technique provided the present application, the noise generated in the liquid pump can be efficiently reduced. For example, the liquid pump provided by the present application may be suitable for application to a fuel pump supplying fuel of an automobile. This liquid pump is useful for reducing a noise in the automobile requiring quietness.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical cross-sectional view of a fuel pump.

FIG. 2 is a sectional view taken along a line II-II shown in FIG. 1.

FIG. 3 is a graph showing a correlation between an analysis result and an experiment result.

FIG. 4 is isograms showing a correlation between two barometers (i.e., σ′/(average of θ) and C′) and spectrum peak value of the pressure variation.

FIG. 5 is isograms showing a correlation between numbers of concavities with identical pitch angles and the spectrum peak value of the pressure variation.

FIG. 6 is isograms showing a correlation between the numbers of concavities with identical pitch angles and a pump efficiency.

FIG. 7 is a graph showing an experiment result regarding a noise pressure generated in a fuel pump comprising a regular pitch impeller.

FIG. 8 is a graph showing an experiment result regarding a noise pressure generated in a fuel pump comprising an irregular pitch impeller.

EMBODIMENT

An embodiment of the present teaching will be described below with reference to the drawings. A fuel pump of the present embodiment is a fuel pump for an automobile, however, it should be understood that the teaching disclosed herein may suitably be applied to other purposes. The fuel pump is used within a fuel tank in order to supply fuel to an engine of an automobile. As shown in FIG. 1, the fuel pump 10 comprises a motor unit 12 and a pump unit 14. The motor unit 12 and the pump unit 14 are contained within a housing 16. The motor unit 12 comprises a rotator 18. The rotator 18 comprises a shaft 20, a layered iron core 22, a coil (not shown) and a commutator 24. The layered iron core 22 is fixed on the shaft 20. The coil is coiled around the layered iron core 22. The commutator 24 is connected with an end of the coil. The shaft 20 is supported by bearings 26, 28 in a manner that a rotation relative to the housing 16 is allowed. A permanent magnet 30 that surrounds the rotator 18 is fixed inside the housing 16. A terminal (not shown) is located on a top cover 32 which is attached to an upper part of the housing 16. By the terminal, electricity is supplied to the motor unit 12. The rotator 18 rotates when the electricity is supplied to the coil via a brush 34 and the commutator 24.

The pump unit 14 is contained within a lower part of the housing 16. The pump unit 14 comprises an impeller 36. The impeller 36 is a substantially circle plate. As shown in FIG. 2, an opening 39 is formed at a center of the impeller. The shaft 20 is engaged with the opening 39 in a manner that a rotation relative to each other is inhibited. As a result, the impeller 36 rotates by a rotation of the shaft 20. N sets (e.g., n=39 but not limited hereto) of concavities 37 are formed at a circumference edge of the impeller 36. In FIG. 2, a concavity 37 (1) means a first concavity 37. Similarly, concavities 37 (2) and 37 (n) mean a second concavity and an n^(th) (39^(st) in the present embodiment) concavity 37 respectively. That is, in the present embodiment, the concavities 37 are numbered in an ascending sequence along a rotation direction (an arrow 60 shown in FIG. 2) of the impeller 36 from the first concavity 37 (1). The n (=39) sets of the concavities 37 are disposed alongside in the circumference edge of the impeller 36 and are intermittently arranged around the entire circumference edge of the impeller 36. Each of fins 37 a is formed between two sets of the concavities 37 (in other words, between adjacent concavities 37). All of the n (=39) sets of the fins 37 a are formed with basically the same shape. The concavities 37 are formed such that pitch angles θ between the adjacent sets of concavities are inhomogeneous. The pitch angle θ_(i) means an angle between an i^(th) first line and an i^(th) second line. The i^(th) first line is a line connecting a rotation center of the impeller 36 and a center of a i^(th) concavity 37 along the circumference edge of the impeller 36. The i^(th) second line is a line connecting the rotation center of the impeller 36 with a center of i+1^(th) concavity 37, which is adjacent to the i^(th) concavity 37, along the circumference edge of the impeller 36. In the impeller 36, a pitch angle θ_(i) between i^(th) concavity 37 (i) and i+1^(th) concavity 37 (i+1) is equal to one or more pitch angles θ_(m) of the n sets of concavities 37. In addition, the i is any integer of 1 to n. Further, with the circular arrangement of the concavities along the circumference edge of the impeller 36, where in case of i+1=n+1, then i+1=1. Furthermore, the m is any integer of 1 to n and other than i. Furthermore, formulas 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35 are satisfied. Note that, σ′, average of θ and C′ are defined as below.

${{average}\mspace{14mu} {of}\mspace{14mu} \theta \text{:}\mspace{14mu} \overset{\_}{\theta}} \equiv {\sum\limits_{i = 1}^{n}\; {\theta_{i}/n}}$ $\sigma^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\sigma_{i} - \overset{\_}{\sigma}} \right)^{2}} \right)/n}$ $\overset{\_}{\sigma} \equiv {\sum\limits_{i = 1}^{n}\; {\sigma_{i}/n}}$ $C^{\prime} \equiv \sqrt{\sum\limits_{j = 1}^{n}\; {\left( C_{j} \right)^{2}/n}}$ $C_{j} \equiv {\frac{1}{n\; \theta^{\prime \; 2}}{\sum\limits_{i = 1}^{n}\; {\left( {\theta_{i} - \overset{\_}{\theta}} \right) \cdot \left( {\theta_{i + j} - \overset{\_}{\theta}} \right)}}}$ $\theta^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\theta_{i} - \overset{\_}{\theta}} \right)^{2}} \right)/n}$

Here, σ′ means a standard variation of a difference between the adjacent pitch angles σ_(i)=θ_(i+1)−θ_(i). σ′/(average of θ) is a barometer (index) for evaluating a variability of the adjacent pitch angles. Greater σ′/(average of θ) indicates greater variability of the adjacent pitch angles. The value of σ′/(average of θ) contributes mainly to a noise magnitude of a basic frequency. The basic frequency of the noise is determined by a total number of the concavities and a number of rotations. Furthermore, C′ is a barometer (index) for evaluating a variability of the pitch angles along the entire circumference of the impeller 36. A value of C′ nearing zero indicates that the variability of the pitch angles in the entire circumference of the impeller 36 is great. The value of C′ contributes mainly to the noise magnitude of a frequency lower than the basic frequency.

Furthermore, the concavities 37 may optionally satisfy another formula: 0.1<(a number of pitch angles being equal to each other)/(the total number of the concavities n (=39))<0.5.

A pump casing containing the impeller 36 comprises a discharge side casing 38 and a suction side casing 40. In the discharge side casing 38, a channel 38 a is formed at an area facing the circumference edge of the impeller 36. The channel 38 a faces a circumference surface and the circumference edge of an upper surface of the impeller 36. The channel 38 a is formed in a substantially C-shape. The channel 38 a elongates from an upper stream end to a lower stream end along the rotation direction of the impeller 36. In the discharge side casing 38, a discharge opening 50 is formed from a lower stream end of the channel 38 a to an upper surface of the discharging side casing 38. The discharge opening 50 communicates an inside of the pump casing with an outside of the pump casing (i, e., an inner space of the motor unit 12).

In the sucking side casing 40, a channel 40 a is formed at an area facing the circumference of the impeller 36. A part of the channel 40 a faces a circumference edge of a lower surface of the impeller 36. The channel 40 a is connected with the channel 38 a at a circumference side of the impeller 36. The channel 40 a, as well as the channel 38 a, are formed in a substantially C-shape and elongate from the upper stream end to the lower stream end along the rotation direction of the impeller 36. In the suction side casing 40, a suction opening 42 is formed from a lower surface of the suction side casing 40 to an upper stream end of the channel 40 a. The suction opening 42 communicates the inside of the pump casing with an outside of the pump casing (i.e., an outside of the fuel pump 10). A flow path 44, encompassing the circumference of the impeller 36, is formed by the concavities 37, the channel 38 a and the channel 40 a.

In the casing 38 and 40, an isolating wall 41 is disposed between the suction opening 42 and the discharge opening 50. The isolating wall 41 is disposed in order to prevent the fuel to flow from a side of the discharge opening 50 toward a side of the suction opening 42. Therefore, a surface of the isolating wall 41 facing the circumference of the impeller 36 is closer to the circumference edge of the impeller 36 than a surface of the casing 38, 40 facing the circumference of the impeller 36.

When the impeller 36 rotates within the pump casing 38, 40, the fuel is sucked from the suction opening 42 into the pump unit 14 and flows through the flow path 44. Pressure of the fuel is raised while flowing through the flow path 44, and the fuel is discharged from the discharge opening 50 into the motor unit 12. The fuel discharged into the motor unit 12 passes through the motor unit 12 and is discharged from a port 48 formed at the top cover 32 to an outside of the fuel pump 10.

In the fuel pump 10, the concavities 37 of the impeller 36 satisfy the formulas 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35. Therefore, the noise generated in the fuel pump 10 is reduced to a lower level than a noise generated in a fuel pump comprising an impeller having uniform pitch angles of the concavities.

In the fuel pump 10, the concavities 37 of the impeller 36 further satisfy 0.1<(a number of pitch angles being equal to each other)/(the total number of the concavities n (=39))<0.5. Therefore, in the fuel pump 10, the noise generated in the fuel pump 10 is further reduced than the noise generated in the fuel pump comprising the impeller having the uniform pitch angles of the concavities. Furthermore, in the fuel pump 10, a reduction in a pump efficiency of the liquid pump is inhibited.

In the fuel pump 10, each pitch angle θ_(i) has one or more corresponding pitch angles θ_(k) (i≠k) having an identical angle value. As a result, a noise component generated due to the concavity 37 corresponding with the pitch angle θ_(i) is decayed by the one or more concavities 37 corresponding with the pitch angle θ_(k). Therefore, the noise generated due to the concavities 37 corresponding to the pitch angle θ_(i) is reduced.

(Analysis of a Relationship Between Pitch Angle of Concavities and Noise Generated in Fuel Pump)

Results of an analysis performed by the inventors will be described below. The results of the analysis conducted regarding the relationship between the pitch angles θ of the concavities 37 and the noise generated in fuel pump 10 will be described first.

(Method for Determining Alignment of Pitch Angles of Concavities)

First, a method for determining an alignment of the pitch angles of the concavities 37 of the impeller 36 used in the present analysis will be described. In the present analysis, a plurality of combinations of a number of the concavities 37 of the impeller 36, a minimum pitch angle θmin, a maximum pitch angle θmax and differences of the pitch angles was determined, and then, the number of each of the pitch angles was determined. Table 1 shows one example of the number of pitch angle θ for each of the determined pitch angles with the following conditions: the number of the concavities 37 is 39, the minimum pitch angle θmin is 8 degrees, the maximum pitch angle θmax is 10.5 degrees and the difference of the pitch angles is 0.5 degrees were determined.

TABLE 1 Number of Concavities: 39 θ_(min) θ_(max) Pitch Angle 8 8.5 9 9.5 10 10.5 Number 5 6 8 10 6 4

In accordance with the above-mentioned method, 10,000 combinations have been determined. Next, a plurality of alignments of the pitch angles has been determined. The alignments for pitch angles mean how the pitch angles are aligned along the circumference edge of the impeller. In the present embodiment, 100,000 alignments for the pitch angles on average have been determined for each of the ten thousand combinations. That is, in the present analysis, the analysis performed on 10,000×100,000 impellers 36 of which alignments for the pitch angles are different from one another. These impellers 36 are collectively termed as an “irregular pitch impeller” below.

(Analysis Method)

First, a fuel pump comprising impeller 36 having the concavities aligned with a uniform pitch angle (θ=7.5 degrees) (hereinbelow termed a “regular pitch impeller”) was subjected to a CAE analysis in the present analysis. In the present analysis, a pressure variation of the fuel was calculated as a function of time. The pressure variation of the fuel means a temporal change in the pressure of the fuel within the concavities 37 when the respective concavity 37 of the impeller 36 passes from the side of the discharge opening 50 to the side of the suction opening 42 of the isolating wall 41. Next, for each of a plurality of irregular pitch impellers 36, the pressure variation of the fuel was calculated as the function of time by using a result of the pressure variation for the regular pitch impeller. In particular, a time axis of the calculated temporal change of the pressure variation was adjusted in accordance with sizes of the aligned pitch angles so as to calculate a pressure variation waveform when the irregular pitch impeller 36 is rotated 360 degrees.

Next, an FFT (Fast Fourier Transform) analysis was performed on the pressure variation waveform calculated in accordance with the alignment of the pitch angles for a spectral resolution. As a result, a spectrum peak value of the pressure variation was calculated.

(Studying for Correlation Between Analysis and Experiment)

Next, a correlation between the experimental results (i.e., results acquired by measuring an actual product) and the analysis results acquired by performing the above mentioned analysis method for the impeller using the experiment was calculated so as to confirm an effectiveness of the above mentioned analysis method. Here, the correlation between the spectrum peak value of the pressure variation of the fuel acquired by the above mentioned analysis and a spectrum peak value of noise pressure generated in the fuel pump 10 acquired by the experiment was studied. FIG. 3 is a graph showing the correlation between the spectrum peak value of the noise pressure acquired by the experiment and the spectrum peak value of the pressure variation acquired by the above mentioned analysis. A horizontal axis of FIG. 3 indicates the spectrum peak value of the pressure variation acquired by the above mentioned analysis. A vertical axis of FIG. 3 indicates the spectrum peak value of the noise pressure acquired by the experiment. As is evident in the graph of FIG. 3, the spectrum peak value of the noise pressure acquired by the experiment is substantially proportional to the spectrum peak value of the pressure variation acquired by the above mentioned analysis. Furthermore, the coefficient of the correlation between the spectrum peak value of the noise pressure acquired by the experiment and the spectrum peak value of the pressure variation acquired by the above mentioned analysis is 0.79. Therefore, it is found that there is a strong correlation between the spectrum peak value of the noise pressure acquired by the experiment and the spectrum peak value of the pressure variation acquired by the above mentioned analysis. The effectiveness of the above mentioned analysis was confirmed. In addition, it was found that the less the spectrum peak value of the pressure variation acquired by the above mentioned analysis, the smaller the noise generated in the fuel pump 10.

(Studies on σ′/(Average of θ) and C′ Corresponding to Pressure Variation)

Next, from the analysis results acquired by the present analysis, a correlation between σ′/(average of θ) and the spectrum peak value of the pressure variation acquired by the analysis as well as a correlation between C′ and the spectrum peak value of the pressure variation acquired by the analysis were studied. FIG. 4 is isograms showing a relation between σ′/(average of θ) and the spectrum peak value of the pressure variation acquired by the present analysis. The isograms of FIG. 4 further show a relation between C′ and the spectrum peak value of the pressure variation acquired by the analysis. A horizontal axis of FIG. 4 indicates σ′/(average of θ). A vertical axis of FIG. 4 indicates C′. In FIG. 4, the isograms indicate values of 20 log₁₀ (PI/PR). In addition, PR is an analysis result (a constant value) of the spectrum peak value of the pressure variation acquired from the fuel pump 10 comprising the regular pitch impeller. PI is an analysis result of the spectrum peak values of the pressure variation acquired from the fuel pump 10 comprising the irregular pitch impeller.

FIG. 4 shows that the spectrum peak values of the pressure variation have a strong correlation with σ′/(average of θ) and C′. Furthermore, in a case of 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35, the spectrum peak values of the pressure variation are found less than the spectrum peak values of the fuel pump 10 comprising the regular pitch impeller 36. From this result, the noise generated in the fuel pump 10 is reduced in the case of 0.05≦σ′)/(average of θ)≦0.30 and 0.15≦C′≦0.35. As is obvious from FIG. 4, the effect of reducing the noise is higher in a case of 0.20≦σ′/(average of θ)<0.30 and 0.20≦C′≦0.30.

(Studies on Number of Pitch Angles being Equal with Respect to Pressure Variation)

Next, from the analysis results acquired by the analysis, a relationship between number of pitch angles being equal and the spectrum peak values of the pressure variation of the fuel was studied. Here, the number of the pitch angles being equal is defined as N, the minimum value of N is defined as Nmin and the maximum value of N is defined as Nmax. The spectrum peak values of the pressure variation were evaluated using barometers Nmin/n (n=total number of the concavities) and Nmax/n. In a case of the pitch angle θ=8 degrees in the Table 1, N is equal to 5. Similarly, in cases of the pitch angle θ=8.5, 9, 9.5, 10, 10.5 degrees in the Table 1, N is equal to 6, 8, 10, 6, 4 respectively. In these cases, Nmin is equal to 4 and Nmax is equal to 10. FIG. 5 is isograms showing the relationship between the spectrum peak value of the pressure variation acquired by the analysis and the barometers of Nmin/n and Nmax/n. A horizontal axis of FIG. 5 indicates Nmin/n. A vertical axis of FIG. 5 indicates Nmax/n. In FIG. 5 as well as FIG. 4, the isograms indicate values of 20 log₁₀ (PI/PR). In addition, in a case where Nmin and Nmax are identical, the spectrum peak values of the pressure variation (PI) are different from each other as a result of the alignment of the pitch angles. Therefore, the value of 20 log₁₀ (PI/PR) was calculated using an average of a plurality of the spectrum peak values of the case where Nmin and Nmax are identical.

As is obvious from FIG. 5, in a case of Nmax/n≦0.5, 20 log₁₀ (PI/PR) was smaller. Therefore, the fuel pump 10 comprising an impeller 36 satisfying N/n≦0.5 further reduces the spectrum peak value of the pressure variation than the fuel pump comprising the regular pitch impeller 36. That is, as is obvious from the analysis results, in the case of N/n≦0.5, the noise generated in the fuel pump 10 is reduced.

(Studies on Number of Pitch Angle being Equal with Respect to Pump Efficiency)

Next, from the analysis results acquired by the present analysis, a relationship between the number of pitch angles being equal and pump efficiency was studied. Here, the pump efficiency was evaluated using the barometers Nmin/n and Nmax/n. FIG. 6 is isograms showing the relationship between the pump efficiency and the barometers of Nmin/n and Nmax/n. A horizontal axis of FIG. 6 indicates Nmin/n. A vertical axis of FIG. 6 indicates Nmax/n. In FIG. 6, the isograms indicate values of (ηI/ηR). In addition, ηR is an analysis result (a constant value) of the pump efficiency acquired from the fuel pump 10 comprising the regular pitch impeller 36. ηI is an analysis result of the pump efficiency acquired from a fuel pump 10 comprising the irregular pitch impeller 36.

As is obvious from FIG. 6, in a case of 0.1≦Nmin/n, (ηI/ηR) was found to be relatively greater. Therefore, the fuel pump 10 comprising an impeller 36 satisfying 0.1≦N/n inhibits to reduce the pump efficiency better than the fuel pump comprising the regular pitch impeller 36. That is, as is obvious from the above mentioned results, in the case of 0.1≦N/n≦0.5, the noise generated in the fuel pump 10 is reduced while the reduction in the pump efficiency is well inhibited.

(Practical Comparison Between Fuel Pump Comprising Regular Pitch Impeller and Fuel Pump Comprising Irregular Pitch Impeller in Actual Products)

An experiment using the fuel pump 10 comprising the regular pitch impeller 36 and the fuel pump 10 comprising the irregular pitch impeller 36 was performed. In this experiment, the impellers 36 were rotated by 6000 rpm which is an intermediate value of an actual number of rotation (3000 rpm to 9000 rpm) when the fuel pump 10 is actually used. In this experiment, the noises generated in the fuel pumps 10 were compared.

The pitch angles of the regular pitch impeller 36 prepared for this experiment are 7.5 degrees. The concavities 37 of the irregular pitch impeller 36 prepared for this experiment are formed by pitch angles shown in Table 2. The pitch angles of the concavities 37 of the irregular pitch impeller 36 satisfy with both 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35,

TABLE 2 Concavity Number 1 2 3 4 5 6 7 8 9 10 11 12 Pitch Angle(°) 7.5 8.5 7.5 8.5 7.5 9 9 7.5 7.5 8.5 7.5 9 Concavity Number 13 14 15 16 17 18 19 20 21 22 23 24 Pitch Angle(°) 7.5 8.5 7.5 8.5 7.5 8.5 7.5 8.5 9 9 9 8.5 Concavity Number 25 26 27 28 29 30 31 32 33 34 35 36 Pitch Angle(°) 7.5 9 7.5 9 9 9 9 7.5 9 9 9.5 9 Concavity Number 37 38 39 40 41 42 43 Pitch Angle(°) 9 7.5 9 9 7.5 9 9

FIG. 7 shows measurement results of the noise generated in the fuel pump 10 comprising the regular pitch impeller 36. In addition, five sets of the fuel pumps 10 were prepared and measured respectively. FIG. 7 includes measurement results of 5 sets of the fuel pumps 10 comprising the regular pitch impeller 36, FIG. 8 shows measurement results of the noise generated in the fuel pump 10 comprising the impeller 36 on which the concavities 37 are formed by the pitch angles shown in Table 2. Horizontal axes of FIGS. 7 and 8 indicate frequency of the noise generated in the fuel pumps 10. Vertical axes of FIGS. 7 and 8 indicate loudness (dB) of the noise generated in the fuel pumps 10. A broken line 100 of FIG. 8 indicates a peak value of the noise generated in the fuel pump 10 comprising the regular pitch impeller 36. As is obvious from FIGS. 7 and 8, compared with the fuel pump 10 comprising the regular pitch impeller 36, the frequency of the noise generated in the fuel pump 10 comprising the irregular pitch impeller 36 is dispersed, and the peak value of the noise is smaller. That is, compared with the fuel pump 10 comprising the regular pitch impeller 36, the noise generated in the fuel pump 10 comprising the irregular pitch impeller 36 is smaller.

From the present analysis, the noise generated in the fuel pump 10 is found to be reduced as a result that the concavities 37 of the impeller 36 satisfying 0.05≦σ′/(average of θ)≦0.30 and 0.15≦C′≦0.35. Furthermore, the fuel pump 10 in which the concavities 37 of the impeller 36 satisfy 0.1<(the number of the equal pitch angle/the total number of the concavities (e.g., 43))<0.5 is found that the noise generated in the fuel pump 10 is reduced while inhibiting the pump efficiency to be reduced compared with the fuel pump 10 comprising the impeller 36 on which the pitch angles of the concavities 37 are formed homogeneously.

The technological elements disclosed in the present specification and appended drawings have technical utility individually or in various combinations thereof and are not limited to the combinations described in the claims at the time of filing. For example, the technique provided by the present specification may apply various liquid pumps other than the fuel pump which sucks and discharges the fuel. Moreover, the art disclosed in the present specification and appended drawings achieve a plurality of objects simultaneously, and have technical utility by achieving one of these objects. 

1. A liquid pump comprising: a pump casing, and an impeller rotatably disposed within the pump casing, wherein n sets of concavities are formed in an outer circumference of the impeller, the n being an integer of 2 or more, in a case where an angle between an i^(th) first line and an i^(th) second line is a pitch angle θ_(i) and an i^(th) difference of adjacent pitch angles is σ_(i) (σ_(i)=θ_(i+1)−θ_(i)), the i^(th) first line is a line connecting a rotation center of the impeller and a center of i^(th) concavity in a circumferential direction of the impeller, the i being any integer of 1 to n, and the i^(th) second line is a line connecting the rotation center of the impeller with a center of i+1^(th) concavity in the circumferential direction of the impeller, where in case of i+1=n+1, then i+1=1, the pitch angles θ_(i) are inhomogeneous, and for each of the pitch angles θ_(i), there is one or more other pitch angle θ_(k) being equal to the pitch angle θ_(i), the k being any integer of 1 to n and other than i, and following formulas (1) and (2) are satisfied: 0.05≦σ′/(average of θ)≦0.30  (1) 0.15≦C′≦0.35  (2) where ${{average}\mspace{14mu} {of}\mspace{14mu} \theta \text{:}\mspace{14mu} \overset{\_}{\theta}} \equiv {\sum\limits_{i = 1}^{n}\; {\theta_{i}/n}}$ $\sigma^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\sigma_{i} - \overset{\_}{\sigma}} \right)^{2}} \right)/n}$ $\overset{\_}{\sigma} \equiv {\sum\limits_{i = 1}^{n}\; {\sigma_{i}/n}}$ $C^{\prime} \equiv \sqrt{\sum\limits_{j = 1}^{n}\; {\left( C_{j} \right)^{2}/n}}$ $C_{j} \equiv {\frac{1}{n\; \theta^{\prime \; 2}}{\sum\limits_{i = 1}^{n}\; {\left( {\theta_{i} - \overset{\_}{\theta}} \right) \cdot \left( {\theta_{i + j} - \overset{\_}{\theta}} \right)}}}$ $\theta^{\prime} \equiv \sqrt{\left( {\sum\limits_{i = 1}^{n}\; \left( {\theta_{i} - \overset{\_}{\theta}} \right)^{2}} \right)/n}$
 2. The liquid pump as in claim 1, wherein a following formulas (3) and (4) are further satisfied: 0.20≦σ′/(average of θ)≦0.30  (3) 0.20≦C′≦0.30  (4)
 3. The liquid pump as in claim 1, wherein a following formula (5) is further satisfied: 0.1<(a number of pitch angles being equal to each other)/n<0.5  (5)
 4. The liquid pump as in claim 1, wherein the pump casing comprises a channel, a suction opening, a discharge opening, and an isolating wall, the channel faces the concavities of the impeller and elongates from an upper stream end to a lower stream end along the rotation direction of the impeller, the suction opening communicates the upper stream end of the channel with an outside of the pump casing, the discharge opening communicates the lower stream end of the channel with the outside of the pump casing, and the isolating wall is disposed between the suction opening and the discharge opening in order to prevent liquid to flow from a side of the discharge opening toward a side of the suction opening.
 5. The liquid pump as in claim 1, wherein the liquid pump is a fuel pump.
 6. The liquid pump as in claim 1, further comprising a motor drivingly coupled to the impeller. 